{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "S+P Week 1 Lesson 2.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w_XJiOdr-MSM",
        "colab_type": "text"
      },
      "source": [
        "# Lesson 2\n",
        "\n",
        "In the screencast for this lesson I go through a few scenarios for time series. This notebook contains the code for that with a few little extras! :)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "vidayERjaO5q"
      },
      "source": [
        "# Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "XpzEXzbHoQhj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 649
        },
        "outputId": "66bb9c24-66c5-4e8b-fa23-d6f03a88cdae"
      },
      "source": [
        "!pip install -U tf-nightly-2.0-preview"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting tf-nightly-2.0-preview\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/1e/84/0eb5eb3807b851a7282865a5407d0782322f4879ee30c88f7b554127edae/tf_nightly_2.0_preview-2.0.0.dev20190824-cp36-cp36m-manylinux2010_x86_64.whl (88.8MB)\n",
            "\u001b[K     |████████████████████████████████| 88.8MB 3.5MB/s \n",
            "\u001b[?25hRequirement already satisfied, skipping upgrade: six>=1.10.0 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (1.12.0)\n",
            "Requirement already satisfied, skipping upgrade: gast>=0.2.0 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (0.2.2)\n",
            "Collecting tensorflow-estimator-2.0-preview (from tf-nightly-2.0-preview)\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/2d/09/e3a7ee314cdc11368086647c96b3c5d0005b6028a3d75957abc51cbc6dc8/tensorflow_estimator_2.0_preview-1.14.0.dev2019082111-py2.py3-none-any.whl (450kB)\n",
            "\u001b[K     |████████████████████████████████| 450kB 44.4MB/s \n",
            "\u001b[?25hRequirement already satisfied, skipping upgrade: protobuf>=3.6.1 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (3.7.1)\n",
            "Requirement already satisfied, skipping upgrade: termcolor>=1.1.0 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (1.1.0)\n",
            "Requirement already satisfied, skipping upgrade: wrapt>=1.11.1 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (1.11.2)\n",
            "Requirement already satisfied, skipping upgrade: wheel>=0.26 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (0.33.4)\n",
            "Requirement already satisfied, skipping upgrade: absl-py>=0.7.0 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (0.7.1)\n",
            "Requirement already satisfied, skipping upgrade: astor>=0.6.0 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (0.8.0)\n",
            "Requirement already satisfied, skipping upgrade: numpy<2.0,>=1.16.0 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (1.16.4)\n",
            "Collecting tb-nightly<1.16.0a0,>=1.15.0a0 (from tf-nightly-2.0-preview)\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/6c/71/57f72fc6d900f8b224f18ef3342035ae23c1b195053c37199accd7ac9fdf/tb_nightly-1.15.0a20190824-py3-none-any.whl (3.8MB)\n",
            "\u001b[K     |████████████████████████████████| 3.8MB 49.2MB/s \n",
            "\u001b[?25hCollecting opt-einsum>=2.3.2 (from tf-nightly-2.0-preview)\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/c0/1a/ab5683d8e450e380052d3a3e77bb2c9dffa878058f583587c3875041fb63/opt_einsum-3.0.1.tar.gz (66kB)\n",
            "\u001b[K     |████████████████████████████████| 71kB 31.9MB/s \n",
            "\u001b[?25hRequirement already satisfied, skipping upgrade: grpcio>=1.8.6 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (1.15.0)\n",
            "Requirement already satisfied, skipping upgrade: keras-preprocessing>=1.0.5 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (1.1.0)\n",
            "Requirement already satisfied, skipping upgrade: google-pasta>=0.1.6 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (0.1.7)\n",
            "Requirement already satisfied, skipping upgrade: keras-applications>=1.0.8 in /usr/local/lib/python3.6/dist-packages (from tf-nightly-2.0-preview) (1.0.8)\n",
            "Requirement already satisfied, skipping upgrade: setuptools in /usr/local/lib/python3.6/dist-packages (from protobuf>=3.6.1->tf-nightly-2.0-preview) (41.2.0)\n",
            "Requirement already satisfied, skipping upgrade: werkzeug>=0.11.15 in /usr/local/lib/python3.6/dist-packages (from tb-nightly<1.16.0a0,>=1.15.0a0->tf-nightly-2.0-preview) (0.15.5)\n",
            "Requirement already satisfied, skipping upgrade: markdown>=2.6.8 in /usr/local/lib/python3.6/dist-packages (from tb-nightly<1.16.0a0,>=1.15.0a0->tf-nightly-2.0-preview) (3.1.1)\n",
            "Requirement already satisfied, skipping upgrade: h5py in /usr/local/lib/python3.6/dist-packages (from keras-applications>=1.0.8->tf-nightly-2.0-preview) (2.8.0)\n",
            "Building wheels for collected packages: opt-einsum\n",
            "  Building wheel for opt-einsum (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for opt-einsum: filename=opt_einsum-3.0.1-cp36-none-any.whl size=58500 sha256=bd6c40116cc2a1c0f869437c7a47bc4a1c7705e9ba08d4140e1cee92ac2af43f\n",
            "  Stored in directory: /root/.cache/pip/wheels/91/98/8d/10e3d4e04c959597a411b91acd3695e9e2d210e68ce3427aad\n",
            "Successfully built opt-einsum\n",
            "Installing collected packages: tensorflow-estimator-2.0-preview, tb-nightly, opt-einsum, tf-nightly-2.0-preview\n",
            "Successfully installed opt-einsum-3.0.1 tb-nightly-1.15.0a20190824 tensorflow-estimator-2.0-preview-1.14.0.dev2019082111 tf-nightly-2.0-preview-2.0.0.dev20190824\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "gqWabzlJ63nL",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import tensorflow as tf\n",
        "from tensorflow import keras\n",
        "import pandas as pd"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "sJwA96JU00pW",
        "colab": {}
      },
      "source": [
        "def plot_series(time, series, format=\"-\", start=0, end=None, label=None):\n",
        "    plt.plot(time[start:end], series[start:end], format, label=label)\n",
        "    plt.xlabel(\"Time\")\n",
        "    plt.ylabel(\"Value\")\n",
        "    if label:\n",
        "        plt.legend(fontsize=14)\n",
        "    plt.grid(True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "yVo6CcpRaW7u"
      },
      "source": [
        "# Trend and Seasonality"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "t30Ts2KjiOIY",
        "colab": {}
      },
      "source": [
        "def trend(time, slope=0):\n",
        "    return slope * time"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "iJjc3G1Maefn"
      },
      "source": [
        "Let's create a time series that just trends upward:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "BLt-pLiZ0nfB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "outputId": "6796fe3c-a4c0-428d-8060-637c61924f57"
      },
      "source": [
        "time = np.arange(4 * 365 + 1)\n",
        "baseline = 10\n",
        "series = trend(time, 0.1)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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Yuu8wFw3pyq8nDiKlQ7zXpUkEUDgTERFpYN2uQ8xamMfrRXsYkJTA0988gzP7dfK6LIkg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\ngg==\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "WKD4nh9sauBf"
      },
      "source": [
        "Now let's generate a time series with a seasonal pattern:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "89gdEnPY1Niy",
        "colab": {}
      },
      "source": [
        "def seasonal_pattern(season_time):\n",
        "    \"\"\"Just an arbitrary pattern, you can change it if you wish\"\"\"\n",
        "    return np.where(season_time < 0.4,\n",
        "                    np.cos(season_time * 2 * np.pi),\n",
        "                    1 / np.exp(3 * season_time))\n",
        "\n",
        "def seasonality(time, period, amplitude=1, phase=0):\n",
        "    \"\"\"Repeats the same pattern at each period\"\"\"\n",
        "    season_time = ((time + phase) % period) / period\n",
        "    return amplitude * seasonal_pattern(season_time)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "7kaNezUk1S9l",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "outputId": "15e56bf4-4736-47fe-98b1-af9ad3e5a8c1"
      },
      "source": [
        "baseline = 10\n",
        "amplitude = 40\n",
        "series = seasonality(time, period=365, amplitude=amplitude)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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vccny8yrRhCF7rl1bInHIXseuOX80iEhzmZrhUgwyaNONGinD4WlsjUcsDtHd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\nSpCSNBEREZESpCRNREREpAT9P/A43mQgac2uAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "-Vo433h0bDLD"
      },
      "source": [
        "Now let's create a time series with both trend and seasonality:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "AyqFdaIN1oy5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "outputId": "a6ce184c-4d8b-4032-cc57-906e454ee30a"
      },
      "source": [
        "slope = 0.05\n",
        "series = baseline + trend(time, slope) + seasonality(time, period=365, amplitude=amplitude)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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b3s/bbT0cb+3hZGsP+97qpfUnTzIwfHnFdV5GhOVleTxwcwVLy3JZXubvn+16lKSJiEzA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\n1IVM0iRJkrqQSZokSVIX+j981lKSgQHz8AAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YVdJ2jNN8OHk",
        "colab_type": "text"
      },
      "source": [
        "# Noise"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "V4taP424sces"
      },
      "source": [
        "In practice few real-life time series have such a smooth signal. They usually have some noise, and the signal-to-noise ratio can sometimes be very low. Let's generate some white noise:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "3kD3_zjVscBH",
        "colab": {}
      },
      "source": [
        "def white_noise(time, noise_level=1, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    return rnd.randn(len(time)) * noise_level"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "aLvBwrKrtDzo",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "outputId": "56860561-8575-4610-e951-f88790238311"
      },
      "source": [
        "noise_level = 5\n",
        "noise = white_noise(time, noise_level, seed=42)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, noise)\n",
        "plt.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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G7CNHj2w0vrbsbB/UkIu4EoBK5qaIdiZL90cvrsP4WyZjOJc3j6fHgs+XhIdm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Omw2mrp2SPqwsoO4YB+9ejMYeFohuNFZrPPfJJJ7dwI+Y5P0E3kU3lEQVSrPh8D8JjN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\nQoIaQRAEQRBETCFBjSAIgiAIIqb8f+FFkTNRJfq9AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "GHa6gicgbL74"
      },
      "source": [
        "Now let's add this white noise to the time series:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "2bRDx8K816N9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "outputId": "2cac1f9e-86ed-41af-c462-68dbb940a358"
      },
      "source": [
        "series += noise\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PzNyMz1eXokurLOU6QR6qKuqa0eIWcOtHawPmWUijkSWNIAhCD3URUrkIO65R3JMsaakD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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "a1sQpPjhtj0G"
      },
      "source": [
        "All right, this looks realistic enough for now. Let's try to forecast it. We will split it into two periods: the training period and the validation period (in many cases, you would also want to have a test period). The split will be at time step 1000."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "_w0eKap5uFNP",
        "colab": {}
      },
      "source": [
        "split_time = 1000\n",
        "time_train = time[:split_time]\n",
        "x_train = series[:split_time]\n",
        "time_valid = time[split_time:]\n",
        "x_valid = series[split_time:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "GICxGswL2aqK",
        "colab": {}
      },
      "source": [
        "def autocorrelation(time, amplitude, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    φ1 = 0.5\n",
        "    φ2 = -0.1\n",
        "    ar = rnd.randn(len(time) + 50)\n",
        "    ar[:50] = 100\n",
        "    for step in range(50, len(time) + 50):\n",
        "        ar[step] += φ1 * ar[step - 50]\n",
        "        ar[step] += φ2 * ar[step - 33]\n",
        "    return ar[50:] * amplitude"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "mCaWIWoDGVCL",
        "colab": {}
      },
      "source": [
        "def autocorrelation(time, amplitude, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    φ = 0.8\n",
        "    ar = rnd.randn(len(time) + 1)\n",
        "    for step in range(1, len(time) + 1):\n",
        "        ar[step] += φ * ar[step - 1]\n",
        "    return ar[1:] * amplitude"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "MVM204K66bnC",
        "outputId": "c4aa6c04-3a76-4263-c6b6-cdbe28393e79",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42)\n",
        "plot_series(time[:200], series[:200])\n",
        "plt.show()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Fl3Dr9m1IpXbiuZEjODo8viyuMYbvTx1HYm4KqXc+Arz6ErbeshOph7c6jlEG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\nUUWhKIqiVOT/ASBOYvr9FZaAAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "9MZ2sCmM8XPU",
        "outputId": "5ddde9e9-7434-4d9e-fb4d-9852e4498571",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42) + trend(time, 2)\n",
        "plot_series(time[:200], series[:200])\n",
        "plt.show()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xvdbXGWOiRGQ98Jg1lzUishF4wBiz57Tj3YXjEhQJCQkZ69YNKVf1aG5uJiws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\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "hqx5et9Bzp5e",
        "outputId": "9affa593-b610-4c5f-cc30-758752c0f348",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42) + seasonality(time, period=50, amplitude=150) + trend(time, 2)\n",
        "plot_series(time[:200], series[:200])\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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U/QF4A8gzHu8Dvh6EczuBf9ValwHnA3crpcqA+4C3tdZTgLeNxwBXAlOM2wrg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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "qb5echI7rHqA",
        "outputId": "c9e6b4a5-4ddb-4abd-ff0c-34982cbcf15a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42) + seasonality(time, period=50, amplitude=150) + trend(time, 2)\n",
        "series2 = autocorrelation(time, 5, seed=42) + seasonality(time, period=50, amplitude=2) + trend(time, -1) + 550\n",
        "series[200:] = series2[200:]\n",
        "#series += noise(time, 30)\n",
        "plot_series(time[:300], series[:300])\n",
        "plt.show()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QdRtP7TrDJTPTKMpO4I1jDTywsZzWbgfp8dG8+e1rJzyNEkBE2HC4NP4sobGs\nMAW3hgNVbVwyM83ncU738OuLhIO8fsuyhnM+xPCUUvzy9qUsyE3iJy8c5qtP7eGVQ7V09bl45p1K\nLErR0etknjkA9vsbDvLywVqSJjhd8ombgpr9HKkdapzukceBAN5BfHvONNPV5/SZV396YYW6/gEk\nnPMhRqaU4tNXzuKeq2axfk81WsPfPnMpTrdGKfjnV67kxS9fyZ0rpjMtLY6/nDeDwkSQEsgU8+dt\nFXx3/UF+8+ELeffSvGAnZ1ScLo3Vj09sRkIMBamxvHqojp++eIQfvmchd182Y9BxI61wGA7S46OJ\ntlnoc8pAwqnimzfOxx5lZX5OIpfNzuBPH7+Y+Bibd0lnzzEAuvHIhKZFPnFTSFltO99dfxCAfZWh\nP0jpfA4/SyBglEJ2mCPG/3ng7JDHeNdYD+O2A6UUeeY4ASmBTA0Wi+Lfrp/LTWab3GVzMgZNnXPL\nklxuWZI7bjM/+0zLhJ5dhJQNe6uxmIOdPLPJhhOnS2Pz8wtxYb8vlKd75PkcfvbCCnWeaqxwDoQi\nPEkV1hShteb5fTWsnJ1OXLSNkw2dwU7SqDn8mI3Xo/8vsqqW7iGP8bSBhPv4CU8ACeeqOBGe5BM3\nRZxqc3OyoZN3L8ljVkY8FY1duNzh1ZDubyM6wJKCZK5fkM2SgmSfq8Y5/BiJHg6kCksES3h/c8SI\ntNaUHq1jS5UTm0Vx46IcZmbE0+d0U+3jl3mo8mc9EI8Ym5U/3FXMTYtyae5yeBd96s8RAb2woH8V\nlnydxeSST1yEK6/r4OOP7uTV006uLMogJS7aO5L6RJhVYzlc7lFP41CQatxchyqFRMI4EOhXhRXm\ngVCEn/D+5ogR9V9Y6baLCgFjzW4wemWFE6fb/xKIR6E5vUdl0+DSlnOUI9FDlWc0upRAxGSTT1yE\n88z3tGZJDLcsMbr9pSfEkJ8Sy97KkSccDBVaa1wBBBBPCWSoXmfecSBh3gurIDWO9Phob16FmCzS\nCyvCeer5U2MG3nmXFiazNwwWrPHw5GO0P7LT46NJiYuibIi1q71L2o60yEiIs0dZ2fGd60JqllYx\nNYT3Ty8xIk89//k33qUFKZxu6qLpvDUuQpUnH6O91yulmJedyNGzbYPPGSHjQAAJHiIowv+bI4bl\nqec/v+pnSYExTmJvmIxIP1cCGf2Ncl5OIsdqOwbNieWIkHEgQgSLBJAI56nnHxxAkom2Wdh0tD4I\nqRo9p498+GNeTiIdvc5BAwq9pRppfBYiIPLNiXCeev7zf7nHx9hYNT+L5/fVeG/Oo3Wstp2KSeoK\n7M1HAAFkfk4iAEfPDux1FimXBY/5AAAgAElEQVTjQIQIFgkgEc5XCQRg9bI8Gjp6eaO8IaBz33D/\nZkp+UTqG1PnPm48APrFF2WYAOa/b8rmpTORrIEQg5JsT4c6teTF4X8m8LPJTYvn++oO09Tj8PqfL\nrTnb2jNeSfSLr7YcfyTZo8hMjBlUWnK63SglDdBCBGrEAKKUylZKrVVKvWQ+X6CU+tRY31gpVaiU\n2qiUOqSUOqiU+rK5PU0p9YpSqsz8N9XcrpRSv1ZKlSul9imllo81DVOBtxfWEPdIe5SVX394Gaeb\nunhyxxm/z/n+373Jiv98bbySyDunm/nWM/uGnZvrXG+ywG72MzPiB00g6XDpsB8DIkQw+fPt+RPw\nMuBZfegY8JVxeG8n8DWt9QJgBfAFpdQC4FvAa1rrIuA18znATUCR+bcG+N04pCHiOUb45X7R9DTS\n46NHNa3J+eNH3GOclPGxNytYt/MMO042+TxmpHyMZNYQAcTpcof9KHQhgsmfAJKhtX4KcANorZ2A\na/iXjExrXaO1fsd83A4cBvKB1cBj5mGPAe81H68GHteGt4AUpVTuWNMR6by9l4b55V6QFseZUawP\nkpkYM+B5a7f/1V/nc7s1b5QZbTDP76v2edxwVXH+mJERT0NH34CqOqdbSwO6EGPgz0j0TqVUOqAB\nlFIrgHGdA0MpNQO4ENgOZGuta8xdZ4Fs83E+0L+epdLcVtNvG0qpNRglFLKzsyktLQ04XR0dHWN6\nfSg4ctK4YfZ0dfrMi93Rw7FGt995dTv6mJtqYXmWjXVH+3hp4xbyEgK7s1e0umjq7CPOBhveOc0l\ncQ0k9xs1f7rNxTNlDsqajd8sfT09AV2TzlpjNt5nXt7MzGQrAKfO9KLdzqBd40j4fHlIXkLTROfF\nnwDyVWADMFsptRXIBG4brwQopRKAZ4CvaK3b+i/BqLXWSqlR1Y9orR8GHgYoLi7WJSUlAaettLSU\nsbw+FByiHI4eJTkx3mdedvQc4e3NJ7jiyqv8GhMR9eZrLJ+TyXuW5rHu6HZmXrCUlbPTR5228rp2\nfv7EHpTq4VcfKebeJ3bzi72axz95ibfN4iu/3YrLpegyZ2NPiIsN6Jrk17bzm92bSZs+n5Jl+QC8\n1LCPuNa6oF3jSPh8eUheQtNE52XEu4VZzXQ1cBlwD7BQa71vPN5cKRWFETz+qrX+h7m51lM1Zf5b\nZ26vAgr7vbzA3CaG4U/vpWlpcTjdmho/e1Y53RqrRZGeYFRlNXb2+jx2/Z4qfvz8oQHb1m45yQcf\n2sb3NxykuqWbBz+ynOsXZLNuzQq6el3c/tA2OnudPPB6Ob0ON+u/eLn3tYH2uJ2WbszKW9FwrqrO\n4XZHxDQmQgSLP72w7gI+AlwELAc+bG4bE2UUNdYCh7XW/9Nv1wbgbvPx3cD6ftvvMntjrQBa+1V1\nCR88bSDDVfV7pjw/42PlvkHndLuxWRTpCdEA/Oi5Q3zwoW08ufP0oGO/vG4Pa7ecZPfpZgAOVLXy\nny8eZkdFE1vLG/n4ZTO4ebHRlLW0MIVf3L6Uho5e/nXoLM/treb24gJmZSbgKZgG2uYdY7OSGhdF\nfce5IOl0aZnGRIgx8KcK6+J+j+3AKuAd4PExvvflwJ3AfqXUHnPbfwA/A54yuwqfAj5o7nsRuBko\nB7qAT4zx/acEh9u4SfavGjzfNE8AaeqC2SOf0+XSWC0WUuOMAFLX3kt7j5Ndp5po7nJw8YxULpqe\nBkBijI32Xie/LT3OH+4q5tGtFcRFW1lamMJbJxr5yKXTBpy7eEYqSsF9Lxymz+XmE5fPBOCiaans\nOtVM3xi6b2Ql2qlrO1dacrrdMo2JEGMwYgDRWn+p/3OlVAqwbqxvrLXeAvi6q60a4ngNfGGs7zvV\nOF0jV9PkJtuJsioqGv0tgRhBqX/Prvs/tIz7XjzEz146woz0OEr//Rpaux209zqJsipePVxLTWs3\nb59q4tJZ6fzyg0s53dhFdpJ9wLkT7VHMy07kyNl2iqenMjMj/tz5XzjM7JTBs+r6Kysphrr2cwHE\n4ZJeWEKMRSA/vzqBmeOdEDExHC494lgHm9XCtLQ4TtQPXjNjKC6zDaS/VRdk8ffPXsaVRRlUNnfj\ncmvKzTU4vn3TBWgNv990gorGLoqnp5Jkj2JRfvKQ579oeipgTLXiUZgWx0N3XoR9DGt3ZCbEUN8v\ngDhdbpnGRIgxGLEEopR6DrMLL0bAWQA8NZGJEuPH6fbvJjk7M4Hj9f4NJnSYbSAAP1q9EKtFEWW1\nkJ1k5+bFubxR1kBNazfHzQCy6oIsXj54lj+9WQEY1VTDedfCHDYdq+eWJXnDHjdamUlGANFao5Qy\nxoFIG4gQAfOnDeQX/R47gVNa68oJSo8YZ04/q2lmZyWw8WidOTrbd8BxuzVag9WsFrtr5YwB+6eb\nvZ1ONXZRVtdOjM1CQWoc/3HzBax+cCuAz5KHx1VzM9nyzWtHTPNoZSXa6XO5ae12kBIXjcPllqlM\nhBgDf9pANk1GQkLV6cYuclPsYVvV4XBpv9I+KyMeh0tzprnb2+4wFM+06r5+uc9IN157sqGTTcfq\nWZSfjNWiWFqYwsavl3C2tYcYmzWAnIxdljmCvq69l5S4aJwuTXSgQ9uFEL7bQJRS7UqptiH+2pVS\ngbdkhpGOPs1192/i0a0ng52UgBk9jfwrgQDeaidfPBMe+irV5CTZibZZeG5vNcdqO/jA8gLvvpkZ\n8QENOBwvnilYPO0gRg81CSBCBMrnt0drnai1ThriL1FrnTSZiQyWY80u+pxuNh0Lj1X7huJ3FVaG\nGUBGaEh3jDArrsWiSI2LYvvJJuxRFm5dGjrTlZ0rgRhjQYxGdGkDESJQfv/8UkplKaWmef4mMlGh\n4lizcbPcVdFMj2PM80cGhcPPnkbJcVEkxthGHI3u8mMVvxWzjFLG925dSJI9ahSpnVhZZpfhg1VG\nAdoIrlICESJQ/vTCeg/wS4zp3OuA6Rgz5y6c2KQFX1mzi2ibhV6nm92nW4Ja/RKo0fQ0yk62j7hQ\nlHdp2WGC0k/eu4jvv3shafHR/id0EiTE2LhhQTZ/3HKSOVkJRm8yKYEIETB/fn79GGO9jmNa65kY\ng/zemtBUhYD2HgcVbW5uu6gAi4JtJxqDnaSAOPwYSOiRk2Sntn2EEogZQKKGKYEk2qNCLnh4/Paj\ny1lamMLDm0/Q55RxIEKMhT/fHofWuhGwKKUsWuuNQPEEpyvo/m93FS4Nt19UwOL8ZLYdb2BXRRMt\nXX3BTtqojGa+p6ykGGpHKIE4/FhfJJTZrBbuXDGdEw2dVDZ3y0h0IcbAnwDSYk65/gbwV6XUrzBG\no0csrTWPbzvFjCQLywpTWDk7g3dOt3D777dx3wuHg528UfF3ICEYJZC69t5hVxh0jdCNNxzcuiSX\nJLtReytzYQkRuOG68T6olLoCYyXALoxlbP8JHAfePTnJC45TjV1Ut3SzapoNpRQrZ6fjMgfQPbev\nesCqdqHOmMrEzwCSbMfp1jR2+i5ledtAwrjx2R5l5f1m92LphSVE4Ia7CxwD/hs4iDFD7mKt9WNa\n61+bVVoRa0ZGPG/9xypW5Bm/Ui+ekUpijI1r52fR43CzYY/vpVdDjdPtHra9or+sRKOXUm2b72os\nf9pAwsGHLzE6EkovLCECN9w4kF9prVdiLCbVCDyilDqilPqeUmrupKUwSBLtUd6bZFy0jc3fuIY/\n3lVMRkI0B6rGdUXfCeVw+t8LKyfZCCDD9cQK9zYQj3k5ify/Wy7gfRfmBzspQoQtf1YkPKW1/rnW\n+kLgw8D7MLrxTimp8dFYLIrCtDhON/k37XkocIxizYscc5zEcD2xIqENxOPTV85iccHw83IJIXzz\nZ0VCm1Lq3UqpvwIvAUeB9094ykJUYWqc3yv3hQKnS/td3ZSREI1FMWxPrEhoAxFCjI/hGtGvV0o9\nAlQCnwFeAGZrre/QWq/39bpIV5gWS3VLj3ep2FA30uy6/dmsFjISYqht873GeaS0gQghxm64kejf\nBv4GfE1r3TxJ6Ql5halxuNyamtYe71riocyzpK2/cpLtnB2mEd0ZIW0gQoix8xlAtNbjvyBDBPCu\nH97cFRYBxJ8lbfvLSrRTOUwV3UjTuQshpg6pyB4lT9A4EyYN6U4/lrTtLyc5xq9uvNIGIoSQu8Ao\n5SbbsVoUFY3hEUAcoxiJDkZPrOYuh8/Zh50jrAcihJg6JICMks1qYUFuEm+fCo9mIX/XA/HwTHle\n56Mh3dMGIlVYQggJIAFYOTudPadbQn6NEK21OZ376Eog4HssiJRAhBAeEkACsHJWOn0ud8iXQpwB\ndLkdaTS6tIEIITzkLhCAi2emYbUotof4GiFOz+qBoyiBZI8wH5aUQIQQHhJAApAQY6MwNZYTDaE9\nq71n/fLRjANJirWRHh/Na4fr0HrwtO7SBiKE8JAAEqCC1Dgqm7uDnYxheUogo+mFpZTiK9cVse1E\nI78tPT5oxP25qUwkgAgx1QU1gCilHlFK1SmlDvTblqaUekUpVWb+m2puV0qpXyulypVS+5RSy4OX\ncihIjQ2DABJYaeEjl07nmnmZ/PfLR/lt6fEB+7yTKUobiBBTXrDvAn8Cbjxv27eA17TWRcBr5nOA\nm4Ai828N8LtJSuOQClJjaejoDemeWA5vI/roLrPVonjk4xczPyeRd04P7CggJRAhhEdQA4jWejPQ\ndN7m1cBj5uPHgPf22/64NrwFpCilcicnpYMVpBoj0kO1FFLb1jOm9gqlFLOzEjhRP7Cdx3NOWclP\nCDHcZIrBkq21rjEfnwWyzcf5wJl+x1Wa22r6bUMptQajhEJ2djalpaUBJ6Sjo8Pn6+ubjZLHi5ve\nYklmaP037jzr5ME9vdy5IBqAY0ePsCixZ9T/F9bOPs40OXjl9Y3ersBlx43lbrdueSMoM/IOd03C\njeQlNEle/Bdad77zaK21UmpwV6DhX/Mw8DBAcXGxLikpCfj9S0tL8fX6+a093Lf9NdIKiyhZMT3g\n95gI9z+4FeilNSoDqGbpooXENh71mRdfWlOq2HB8D9MXFjM3OxGAfa4yKDvGtSUlQanGGu6ahBvJ\nS2iSvPgv2G0gQ6n1VE2Z/9aZ26uAwn7HFZjbgiIrMYYoqwq5KqwzTV3sq2wB4FBNGzC6cSD9zcpI\nAOB4XYd3m6cNRJpAhBChGEA2AHebj+8G1vfbfpfZG2sF0NqvqmvSWSyK/JTYYac+D4Zdp5rQGvJT\nYik3b/xFWQkBnWtmZjzAgPEuxvTwCqUkgggx1QW7G+8TwDZgnlKqUin1KeBnwPVKqTLgOvM5wIvA\nCaAc+APw+SAkeYCJGAuy7Xgjd67dzvfWH+C5vdWsfmDLkKsfut2ax7dVcOtv3uDuR3bQ3uMA4Fht\nB1FWxc2LcwCYn5PIjIz4gNKSEGNjRnocm47Ve7e53KObHl4IEbmC2gaitf6wj12rhjhWA1+Y2BSN\nTkFqLK8erhv5wFF4dnclb5Q18EZZA9uON1JW18HB6jaWFqYMOO7RNyv48fOHKMpKYNOxeraWN3Dj\nolzKatuZmRHP4gLj+BsW5owpPR+5dBo/ffEIB6tbWZiXbEzOKGNAhBCEZhVW2JiIsSBVLd2kxkUB\nUGZWQT269SQ/fO4gbrP9ob3HwQOvl3FlUQbP33sFMTYL2082eV9TlJXIZbPTuXxOOrdfVDCm9Hyo\neBqxUVae3Gl0gHO5tYwBEUIAEkDGZCLGglQ1d3PZnAwK02K92/5vTzWPbq2gqsV4n+f21tDc5eCr\n188lxmZl+bRUdlY00d3n4nRTF0XZCWQkxPDXT68Y87K7yXFRLJ+ewu7TRsO8w2wDEUIICSBjUJBq\n3OT9bUjvdbq8bRVDcbs11S09FKTEcvXcTCwK3rUw27u/rK4dgN2nm0mLj2aZWa11ycw0DlW38fe3\nz6A13i6342VxfgpHzrbR63RJG4gQwksCyBh4SiBn/CiBVLV0s+B7L/OJR3f6PKaho5c+l5uC1Fi+\nvGouj3/yUu5dVcSHio3ey2W1RpXW3soWlhQke3tC3bw4lxible+uP0hBaiwrZqWPNWsDLC1IxuHS\nHK5plzYQIYRXSA8kDHXesSBNI5dAfvrCYVxuza5TzXT1OYmLHvxfX2lWUeWnxpKZGENmYgwAP79t\nCRuP1lFW10FHr5Oyug5uWnRuFpd5OYls/sY1bD/ZyDXzsoiPGd/LusQs6eyvbJE2ECGEl/yUHAOL\nRTEjPd473mI4TZ193sd7z7TS1eekubOPY7XtPL+vGq21ty0lP2Vwu0VRdgJldR0cqGpFa7zVVx6Z\niTHcuiRv3IMHQF6ynbT4aA5UtUkbiBDCS0ogY7QwL4m3Tpw/H+RgTrebBblJHKpp453Tzfx+83Eq\nGjqxR1k5cradHyQcoqGjFzBKIOcrykrk6V1n2GH2tjq/W+9EUkoxIz2OM81dJMdGSRuIEAKQEsiY\nLcpP5mxbD/XtvcMe53Rr0hOimZUZz7qdpyk9Wk9FYxdHzhoN47Mz48lPiWVWZjwJQ5QiFuUn09nn\n4vFtFSwtSCYtPnoisuOTZ9Ck061lPXQhBCABZMwW5iUDcLC6ddjjnC5NlNXCRy6ZRlVzNxkJ0dij\njP/+5754BU/es5It37yGl79y1ZCvv3FRDnHRVho6+iiZlzW+mfBDQWos1S3d9DmlCksIYZAAMkYL\n8pIAOFjdNuxxDpcbq0Xx6Stnsenfr+HZz1/OzYtzmZkRz6J84xxKKZ/LzybE2Hj3kjwArpkfjAAS\nh9OtqWrplkZ0IQQgbSBjlhwbRV6yfcCMtUNxubV3ESbP4L6fvm8xvU633xMTfvm6ImZlxrMkP3ls\niQ6AZ8zLqcbOQQ34QoipSQLIOEhPiKG5q2/YY4YaP2GPsmKPsvr9Pnkpsdxz9eyA0jhWngDicEk3\nXiGEQaqwxkFKXBRNXb5HmIPRCyuc2w7yUs71DJOBhEIIkAAyLtLio2kZqQTiCu8pQOxRVrLMgY1S\nAhFCgASQcZEaFz1goOBQjKqf8P7vvnhGGiABRAhhCO87WohIjYumvceJY4iFnzxcbre3ET1cXbfA\n6P11aIQeZ0KIqUECyDhIizfW72gZph3E6Qr/SQivMcefnG3rCXJKhBChQHphjYOUOGNUeHNXn3cC\nxPM5I2Aa9JS4aD5XMpu52YGtsS6EiCwSQMaBZ1qR5mHaQcK9F5bHN2+cH+wkCCFCRHjXqYSI1H4l\nkKForXG4dEQEECGE8JAAMg5SzTaQZh9tIOZS5th8TFMihBDhSO5o48BTAvHVldfTOyvc20CEEKI/\nCSDjwB5lJTbK6nMwocssgkgVlhAikkgAGSdp8dE0+iiBOF2eACL/3UKIyCF3tHGSnhBNY4ePAOKW\nKiwhROSRADJOMhNivEvSns/plhKIECLyyB1tnGQkxPhc1lYa0YUQkSjsAohS6kal1FGlVLlS6lvB\nTo9HRqLRBuL29NntRxrRhRCRKKwCiFLKCjwI3AQsAD6slFoQ3FQZMhJicLk1Ld2Dx4I4PI3oMg5E\nCBFBwu2OdglQrrU+obXuA9YBq4OcJsAIIMCQ7SBSAhFCRKJwmwsrHzjT73klcGn/A5RSa4A1ANnZ\n2ZSWlgb8Zh0dHX6/vqrJBcCrW3ZQnT5wmdpTbca+I4cOEtd4NOD0jMVo8hLKIiUfIHkJVZIX/4Vb\nABmR1vph4GGA4uJiXVJSEvC5SktL8ff1BXUd/GzHJvJnz6dkWf6AfXvOtMCbW7lw6RJK5mcFnJ6x\nGE1eQlmk5AMkL6FK8uK/cKvCqgIK+z0vMLcFXaZZhTVUTyyXOQ5EVvITQkSScAsgO4EipdRMpVQ0\ncAewIchpAiAp1ka01ULDEIMJzzWiSwARQkSOsKrC0lo7lVJfBF4GrMAjWuuDQU4WAEopMhKiqWsf\nvFqfSwYSCiEiUFgFEACt9YvAi8FOx1CmpcdxsqFz0HYZSCiEiETyk3gczctOpKy2A60HDiY8N5mi\nBBAhROSQADKO5uYk0tHrpLp1YDWWzIUlhIhEckcbR/OyEwE4drZ9wHbPbLxRUoUlhIggEkDGUZEZ\nQI7WDgwgnkZ06cYrhIgkEkDGUXJsFLnJ9kElEE833iiZC0sIEUHkjjbOZmbEc7JxYE8sp0sGEgoh\nIo8EkHE2PT2O041dA7Z5G9GlDUQIEUEkgIyzaWnxNHb20dHr9G7zlECipBeWECKCyB1tnE1PjwPg\nVL9qLE8JxColECFEBJEAMs6mpRkBpH81lieASAlECBFJ5I42zrwlkKZ+AUQa0YUQEUgCyDhLtEeR\nFh89ZBWWDCQUQkQSCSATYHF+Mq8drqPHYaxE6HRprBaFUhJAhBCRQwLIBLjn6lnUtfeybsdpwCiB\nSPWVECLSSACZACtnpbMwL4mXDpwFjDaQKAkgQogIIwFkAiilWJCb5F0bREogQohIJAFkgszMjKeu\nvZeOXidOt1vmwRJCRBy5q02QWRnxAFQ0dOJ0aZnGRAgRcSSATJCZGQkAHK/vwOnWspiUECLiyF1t\ngkxPj0MpONnQidPllhKIECLi2IKdgEhlj7KSnxLLifpOXFoa0YUQkUdKIBNoRno8p5q6cLm0zIMl\nhIg4clebQIVpsVQ2deF0SxWWECLySACZQAWpcTR29tHW7cQmVVhCiAgjAWQCeaZ2P9nYiU3GgQgh\nIozc1SZQoRlA6tt7SYmNCnJqhBBifEkAmUCFqbHex5fNyQhiSoQQYvwFJYAopW5XSh1USrmVUsXn\n7fu2UqpcKXVUKfWufttvNLeVK6W+NfmpHr20+Gjioq0AXD1XAogQIrIEaxzIAeD9wO/7b1RKLQDu\nABYCecCrSqm55u4HgeuBSmCnUmqD1vrQ5CV59JRSFKbG0d7jYHZmQrCTI4QQ4yooAURrfRgYaoGl\n1cA6rXUvcFIpVQ5cYu4r11qfMF+3zjw2pAMIwL2rilBqyLwKIURYC7WR6PnAW/2eV5rbAM6ct/3S\noU6glFoDrAHIzs6mtLQ04MR0dHSM6fUA8ea/paVHx3SesRqPvISCSMkHSF5CleTFfxMWQJRSrwI5\nQ+z6jtZ6/US9r9b6YeBhgOLiYl1SUhLwuUpLSxnL60NJpOQlUvIBkpdQJXnx34QFEK31dQG8rAoo\n7Pe8wNzGMNuFEEIEQah1490A3KGUilFKzQSKgB3ATqBIKTVTKRWN0dC+IYjpFEKIKS8obSBKqfcB\nvwEygReUUnu01u/SWh9USj2F0TjuBL6gtXaZr/ki8DJgBR7RWh8MRtqFEEIYgtUL61ngWR/77gPu\nG2L7i8CLE5w0IYQQfgq1KiwhhBBhQgKIEEKIgEgAEUIIERCltQ52GiaMUqoeODWGU2QADeOUnGCL\nlLxESj5A8hKqJC8wXWudOdJBER1AxkoptUtrXTzykaEvUvISKfkAyUuokrz4T6qwhBBCBEQCiBBC\niIBIABnew8FOwDiKlLxESj5A8hKqJC9+kjYQIYQQAZESiBBCiIBIABlCOC6f259SqkIptV8ptUcp\ntcvclqaUekUpVWb+mxrsdA5FKfWIUqpOKXWg37Yh064Mvzav0z6l1PLgpXwwH3n5gVKqyrw2e5RS\nN/fbN+RyzqFAKVWolNqolDpkLkf9ZXN7WF2bYfIRdtdFKWVXSu1QSu018/JDc/tMpdR2M81PmhPQ\nYk5S+6S5fbtSasaYE6G1lr9+fxiTNR4HZgHRwF5gQbDTNco8VAAZ5237L+Bb5uNvAT8Pdjp9pP0q\nYDlwYKS0AzcDLwEKWAFsD3b6/cjLD4CvD3HsAvOzFgPMND+D1mDnoV/6coHl5uNE4JiZ5rC6NsPk\nI+yui/l/m2A+jgK2m//XTwF3mNsfAj5nPv488JD5+A7gybGmQUogg12CuXyu1roP8CyfG+5WA4+Z\njx8D3hvEtPiktd4MNJ232VfaVwOPa8NbQIpSKndyUjoyH3nxxbucs9b6JNB/Oeeg01rXaK3fMR+3\nA4cxVgsNq2szTD58CdnrYv7fdphPo8w/DVwL/N3cfv418VyrvwOr1BjX2pYAMlg+g5fPHe4DFoo0\n8C+l1NvmEr8A2VrrGvPxWSA7OEkLiK+0h+u1+qJZrfNIv6rEsMmLWfVxIcYv3rC9NuflA8Lwuiil\nrEqpPUAd8ApGCalFa+00D+mfXm9ezP2tQPpY3l8CSGS6Qmu9HLgJ+IJS6qr+O7VRhg3L7nfhnHbT\n74DZwDKgBvhlcJMzOkqpBOAZ4Cta67b++8Lp2gyRj7C8Llprl9Z6GcYqrZcA8yfz/SWADDbcsrph\nQWtdZf5bh7HuyiVAracKwfy3LngpHDVfaQ+7a6W1rjW/9G7gD5yrDgn5vCilojBuun/VWv/D3Bx2\n12aofITzdQHQWrcAG4GVGNWFnrWe+qfXmxdzfzLQOJb3lQAyWFgvn6uUildKJXoeAzcABzDycLd5\n2N3A+uCkMCC+0r4BuMvs8bMCaO1XnRKSzmsHeB/GtQHfyzmHBLOufC1wWGv9P/12hdW18ZWPcLwu\nSqlMpVSK+TgWuB6jTWcjcJt52PnXxHOtbgNeN0uNgQt2T4JQ/MPoQXIMoz7xO8FOzyjTPguj18he\n4KAn/Rh1na8BZcCrQFqw0+oj/U9gVCE4MOpvP+Ur7Ri9UB40r9N+oDjY6fcjL38207rP/ELn9jv+\nO2ZejgI3BTv95+XlCozqqX3AHvPv5nC7NsPkI+yuC7AE2G2m+QDwPXP7LIwgVw48DcSY2+3m83Jz\n/6yxpkFGogshhAiIVGEJIYQIiAQQIYQQAZEAIoQQIiASQIQQQgREAogQQoiA2EY+RAgxEqWUpzsr\nQA7gAurN511a68uCkjAhJpB04xVinCmlfgB0aK1/Eey0CDGRpApLiAmmlOow/y1RSm1SSq1XSp1Q\nSv1MKfVRc02H/Uqp2eZxmUqpZ5RSO82/y4ObAyGGJgFEiMm1FPgscAFwJzBXa30J8EfgS+YxvwLu\n11pfDHzA3CdEyJE2ENXQ3vwAAACnSURBVCEm105tzgmllDoO/Mvcvh+4xnx8HbCg31INSUqpBH1u\n7QchQoIEECEmV2+/x+5+z92c+z5agBVa657JTJgQoyVVWEKEnn9xrjoLpdSyIKZFCJ8kgAgReu4F\nis3V8Q5htJkIEXKkG68QQoiASAlECCFEQCSACCGECIgEECGEEAGRACKEECIgEkCEEEIERAKIEEKI\ngEgAEUIIERAJIEIIIQLy/wEFaEQPUdjDQwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "iBfpCbu6jsaB",
        "colab": {}
      },
      "source": [
        "def impulses(time, num_impulses, amplitude=1, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    impulse_indices = rnd.randint(len(time), size=10)\n",
        "    series = np.zeros(len(time))\n",
        "    for index in impulse_indices:\n",
        "        series[index] += rnd.rand() * amplitude\n",
        "    return series    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "BJ1kXWNLg_BD",
        "outputId": "b65195b6-980b-4844-e523-e188ffe7b4ca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "series = impulses(time, 10, seed=42)\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9q+cZHx/v+r7t2L79dQBGnhihXh/r+nGyztkrVchZhYzQWc5tT+4DYOfOsdxfW7s5W7V5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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "uvMAqSatkcyX",
        "colab": {}
      },
      "source": [
        "def autocorrelation(source, φs):\n",
        "    ar = source.copy()\n",
        "    max_lag = len(φs)\n",
        "    for step, value in enumerate(source):\n",
        "        for lag, φ in φs.items():\n",
        "            if step - lag > 0:\n",
        "              ar[step] += φ * ar[step - lag]\n",
        "    return ar"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "iUv8l8nchJRZ",
        "outputId": "3797e51b-2d6c-4e34-d2c7-da8b3eafc7cb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "signal = impulses(time, 10, seed=42)\n",
        "series = autocorrelation(signal, {1: 0.99})\n",
        "plot_series(time, series)\n",
        "plt.plot(time, signal, \"k-\")\n",
        "plt.show()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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r4YW1+2hp637o6HjhRkNzyBXTh5OW7ONv79Z23qfgCzt2V0wbTmaKn78sr+lx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\nUKgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "5_lx-AlWhT5v",
        "outputId": "c5567a1a-4fba-4f8f-8f15-5ebb834cceee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "signal = impulses(time, 10, seed=42)\n",
        "series = autocorrelation(signal, {1: 0.70, 50: 0.2})\n",
        "plot_series(time, series)\n",
        "plt.plot(time, signal, \"k-\")\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FS51wOk9Nweuq9RLLotlNdPeP5L3QzW/pvBZ6htIc68l7H7Bckls8pxmAg92F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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "nWQ9fvFAOGRB",
        "outputId": "73f7fbb5-e79b-475d-c5cf-7b5d8ebff4de",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "series_diff1 = series[1:] - series[:-1]\n",
        "plot_series(time[1:], series_diff1)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9gCtev5CmRUdxzuKjjqibuzbs4pM/f4J/faKfOdPq+dK7TuScxUdz8rxpR/xm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\nREQkMCUNEREJ7P8D3DhG9byNrLYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "AvUI22RSONQd",
        "outputId": "c419a7b5-b62c-4cdb-aba5-5e13cefa7e1c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        }
      },
      "source": [
        "from pandas.plotting import autocorrelation_plot\n",
        "\n",
        "autocorrelation_plot(series)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f4c50f53278>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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2XVPxxyUi/vaQ57onbakF+OMTSQnj9bsaqE5iRdh96vcByC57l9yy3q9jaska\ny8FpzvDbok1/ILmp8/Dawdq5XXHMxTQVTiehpZrijY93+3fsGrcnfTiNBdPJOriexNb+/fBRiUO0\n904mRWhLH8aBmdcBkL/jn2Qe2ogi+OOT0PgkVARRda5JQBHU7TjVjuPUtXhJzy1EJe7wKwe6yJWg\n/Zx1/vgk6kaeQsnvbg2rUz6c61AagU0i8gZBk0Kq6rfC2Lc3xcDeoOUy4JSeyqiqV0TqgHx3/Xtd\n9i0OdRARuRm4GZyx5y37t8Kx7dQlF9LMIZomHp6WLK6xguZ9JQRPnuLVXXAM1GoqbbnToL2VxPUv\nkuhrpw3oeslje3YFjEygMqEQjU/Cd3AbtbW19KixiuassXj8QlxzNQ2Vnf/D+Xy+jv0Ty9bgmXA2\nDUUnIm1NxNft6/G1vZTAmLOpis8nsXIzTZljia/ZTV0P5bW1gVaSqG7x0TD7c4inkfSVv6HRU0/K\nloV4xp2BlLxJbWsd7fHOb4u6dqEtrZDkHW/RWLEPqdhHQnImzP0BbcOmUbN9GZ7UfOd9EEeVPx1f\nUgb+A1toPLSXjHd/ReNJN1FVfAZtO9c6H+TgmCSOhukTia/ZTcr2ZTQf/wXKj72SjPd/T0Ld3k5l\n24ZPp3XKhSTu/5D24dMgPhF/Wp5z7D3riW88dLhs0eH7wzWkFOKvraVlWF7Hupra2k5fIE1j8sHv\nXnyaNobUso9DnsOA9oLJNM3+EgmVpaRvfBHx9T23mgJ1p94GQM7iu/os31Xw5yTAn5RO66QLSC15\nDfH2HIM/JZvWieeSvOtd4hsP9lgOwJt5+E6iTYl5SG+fbcCTNbXjeW1cFsm1nX/xd41b45NpmXw+\nSfs3kFAX3g+HcLQVHY9n9EnEeRpJ2/KXXs+HLzWXprzJ4PXgTc3jQNEZpG79J+ILus12UNz+pAwa\njr8UTc2hYdhxJJWtIXnXSuJbQtci/CnZtEy9CG/uODQuERJTSC5dRnLZGtrzJ6BJGWhSGpqYiiam\n4U9Mw5c1AhJSwOuBhGRqhs+mtmAGvoxhENe/O8T2b24MwBf+SMxwaijXh1qvqk/3L6pur3sFMF9V\nv+IuXwucoqq3BJXZ7JYpc5e34ySdHwPvqeqz7vrHgX+o6su9HXPKlClaUlLCtY+/z9vbnLmkinNS\nefyGOWwqq+OU8fmMce+8GNDo8TLzx69z2axi/rZxP9efPo7/+mzXlrnDFm8u52vPruXEsbms21PD\nmrvOI9+d2j6UpR8f5MtPOxd1XTZrJA9ddUKn7cuXL++4gKqlzcctf1zH0k+cL8fbLpzCN+dNDPm6\nXp+fuQ8sJykhjgumjeC3K7ZGz1blAAAduklEQVTz8FWzWDArZN7l2sffZ/uhRopyUtmyv45Ft57J\nxGEZIcuu3lnNlb9bxazROWzYW8vi75zJ1BGHJ0/46h/WsOSjg8wozmZjWR0js1Pw+pXjRuWwcnsl\nq+44l2x3epuFG/fzrefX87trT+TC6SM6XmNPVTNff24tW/bX8+trZnPxzCLqW9s56/5lnDo+n99e\ne2JH2YoGD+f9fEVHP8jwrGSmjsgiNy2RVzfs5/4rjuNKt5kuEN+aXTXMmzqMhRv386NLpvHUu7vY\ndshpnvvo7gs7bgPd0ubj5P9ZwoXTR1Df0s57O6p46wfzOmZR6Olcvr2tkvg4YeqITJ798ikdsy+E\n0ujx8tAbW3nsHefiundun8eo3LRu5fZWN1OUnUJCfPeW6uDPCThNc999cQOvbSrnh5+dxk2fGd/j\n8W98cjXLSio4eVweL3711I4bt4Xym+XbuW/xJ5w6IY/tFU2suuOckPEEfOO5tazdXUNCXBzTRmbx\n++vm4PH62H6oiWkjs7rF/ehb2/mf1z5hWGYyK26b161Juast++tYXlLBpceP7Jixoqt3tlXypccP\n11LTkuK59tSxfPOciWSlHB452eb1s35PDT/520fsrWlm8XfO4ncrtvPMqt0UZCTzrXMncunxI0mI\nj+OFf6wgecREPtpfz5KPD9Lk8fLIF2fz2qYDvLphHwBzpwyjMDOZ5IQ4apraqGpqo6LBw9aDDSTG\nx/HZ40aSmZLA2t01bN5fR/BXcUpiHDmpSWSnJpKdmsjkERnMHpPLmZMKeXDJVtbtrmFYVgrHFmVS\nmJFMZkoCIoKq4vM7N91TAoOunL8J8XHs37WNM+bMIiFO3O1uGZx9/Oruq4rfDwnxwjGFGYzJTz/y\nGorbL3GBql7T1wt9CvuA0UHLo9x1ocqUuU1e2UBVmPv26LvnT6a2uZ25Uwr56tnHkJGc0OkLMVhG\ncgKnjs/nL+v3kZGcwJd7+Y8JcPbkQnLSElm7u4Zzpg7rNZkAzJsyjHH5aeyqauZzs0f1WjY1KZ7/\nvXwmJ/+Pc9XypceP7LFsQnwc919xHF9+ag2/XbGd+dNHcMlxPZe/bFYxt728kcqmNh74/PE9JhNw\nJsEEZ8LLy2aN7Hbu7r38OL5bt4xyr5//OHM89S1eXlyzlyUfH+Q/L57akUwALp4xggfy0rh/8Sec\ndkw+WSmJrN9Tw01PfYBf4TfXzOaimYf7eq45ZQy/Xr6df2w6wEUzi2j3+fn+nzbS0u7jd9eeyOqd\n1Xzp1LGML0jH51de33KQlaWV/NvMItKTnf+8b3x0kK+efQw3nj6OT8rruesvmwE4dUIe7+2opr7F\nS5PHR3ldK4+/s4OGVi9fOGk0mSkJXPzw2/z07x/zwOeP73gPPr9yoK6FmqZ23i6t4O1tldx24RSm\nj8zipqc+4NG3d3D7/KmdztGBuhZWllaxu7qZV9aVUVbT0pGgX99ysNPnzOP18as3S/nlm6VkpyZy\n4fThnH5MAc+v3sOCWcV88ZTOd+Res6uarz27ruPWCKt2VPWYUF7fUs6ykgry0pNYvaua836+gqdu\nPDnkl7Oq8tcN+5hZnM0Np4/na8+u5bn393D96eNCvnZDaztvb63k4plFpCXH89x7ezhY38qPF27h\nH5vLWf9f53cq3+b188f39wBwqMHDkyt38o25oX8wrd9Tw8/f2Nrxw/Cxt3fw1I0nc7w70MTvVzaW\n1bJ4Szl/fH8P4/LTWPyds9h6sIEn3tnJo2/v4M/r9vHVsyaQmZLAm58c4p3SSprbfKQlxfPIF2dT\nnJPK3QtmsGBWMfct/oQf/nULP/xr8BX5m8lOTeS4UdncPn8qM4qzmTd1GN+/cAo/e72EDXtrWbe7\nBo/X797iIpmROalcMG04Xzh5DMXupLJ1ze389q3tqMIVJxZTnJPWayL9n8/N7HFbX5a37uSMiQWf\nev++hFNDeQc4R1UjetcmN0FsxbkD5D7gA+CLqrolqMw3gZmq+jURuQqnL+dKEZkO/BE4GRgJLMWZ\nGqbXHtNADaW/Al8sF88s6jQHV0/e2lrB0yt3cftFU5k8PLPP8vtrW3hvRxWfO6G426/Drr/gVJUH\n/lnCzOLsjk713hyoa2FPVTNzxuV13IO+J9VNznxj2amJvZZTVe5/vYTs1ERuOmM8SQm9/2J+8I2t\nPLx0G987fzK3njOx23tcWVrJdU+sZkR2CnPG5rJ4SznDMlN4+qaTGV/Q+bKnmqY2rntiNZv21TGz\nOJuWdh+lhxr56WUz+NKpY7vFcd0Tq3lrawWJ8UJRdir7a1soyklh0a1nkp2aiKqysayOhDih9FAj\n33lxAyJ0/FoUgW/Oncj3L5wCOIMVfvlmKZ8/cRRj89MoPdTIO6VVne5rc+akAn5/3RxSEuP55h/X\nseSjg9x/xXFMKMhgY1ktiz7cz/s7qzuOMa0oi58smM5J4/K4/Nfvsq+2hVe/eQbDM1NYsbWCe/7+\nETsqmphQ4Nz2YFlJRaf3+PBVs8iu3cbcuXNZuHE/t/1pIyNzUvnG3GPYtK+OZ1bt5t9mFlGQkcS1\np43r+LFwqKGV+Q+9zYisFF75xun8YdVuHl66jaSEOC6eOYI5Y/O4eGZRx7/v86v3cOcrm/jZFcfx\n77NH8eWnP2DF1go+M6mQdq+fb507idOOcZo4W9p83PXqJl5Zt4+Ft5xBdmoi5//8LWaOyu4YLPLC\nzafSumcTJ556Buv21PLIm6Ws3lXNEzfM4bn39vD+zmoW3nIGEwozUFV2VzWzcnsVSz8+yNJPDlGQ\nkcwNp4/lzEmF3PL8Omqa2rnnsumMzE7lB3/+kN1VzSTECWdNLuQnl07vlCQ3ldXx479t6YilKDuF\nc48dxpmTCjl1Qn63/wOqytrdNazZ7Uzy2nJwJ1decDrFOam91ugGm67fJ+ESkbBqKOEklGeAY4GF\ndO5D+Xm/o+r+2hcDDwHxwBOq+t8icjfOmOeFIpIC/AHnSv1q4CpV3eHuexdwE+AFvqOqfd7n/tMm\nlFj6tB+AWOvaVLe/roVjCnuu9by/o4oH/lnCnupm5ozN40eXTmNYZvcRbOD8kn1m1S5e31KOiHDt\nqWO5pIfaWpvXz5pd1by1rZJ9tS2Myk3lxjPGhXzt6qY27vzDMqZMGEdBZjLDMpOZPjK70xdRu8/P\nPYs+4oXVe2nz+SnMTOaU8XmcfkwB+RlJTByWwYSC9I4vmYoGD9c9sbrTaLZx+WlcdkIx82eMYFx+\nOimJh3+Nbiqr4wuPrsLj9XcMKR+dl8pPL5vJ2ZOd4do7K5tobPUyoTCdG5/8gNW7qpmWH0dyehbr\n99Ry0rhcfnftHPLSk2ht9/Ffr27m7W2V1DS30e7zc9HMIk4am8tfNuznkwP1LLr1M0xyf/iUlDfw\nv//4mLW7amjweElJjGPisAyS4uNYt6eWMybm88xNpxAfJzR5vNy/+BPe3V7FofpWPF4/2amJ+FWp\na2mn3ad8+9xJfPf8yQC8sq6MO17ZRJs7SmzqiExqGxopb3K+gwoykvjB/KlcOWc0ZTXNXPqrdxHg\nkuNHsnJ7JVsPOk2SwzKTufrkMfzHWRPIcG+Gd6Cuha/+YS0fljn9e6PzUvl/509h7pTCXpsny2qa\nafR4mTI8s1+J4V/h/2V/RDKh/CjUelX9Sb+jirHRo0frPffcE+sw+mWwjoLpy7963D53IEyIylnI\nsrubE/H4hcJkH/mJPnr77qpqi2NDXQrtfmFUqpepmR4Seijf5od3qtL4uC6epIR4pmV6OCWvJWT5\nRq+wsjqNdbUptPrjSIrzc/HwRmZld++gVoXtTYlsb0riUFsCXj+MTvNyVn5TyOl5KtviWVWdiqpT\nq0uJUyZneBib1nmosMcnIMpL+7KdmSFoZWymUJTiZXxaG4lBr13hiefvBzPY1ZxIbqKf0/KamZDW\nTn5S6PPnVyhtSmJ/awInZLd2TNAaDf/qn++uwp16pc+E0lHQuQ0wqtr3zTYGqeLiYr311ls7rUtP\nTyczMxO/38+hQ4e67ZORkUFGRgY+n4+Kiopu2zMzM0lPT8fr9VJZ2f2mUVlZWaSlpdHe3t5txlGA\n7OxsUlNTaWtro7q6+6iQhIQECgoKaG1tDTmiKy8vj6SkJFpaWqir6z6yOz8/n8TERJqbm7vNaApQ\nUFBAQkICTU1NNDR0H/9RWFhIfHw8jY2NNDZ2/6cfNmwYcXFxNDQ00NR0+OI1r9dLQkICI0Y4He11\ndXW0tHS++ZiIMHz4cMD5oLe2dr5QLj4+nsJC51d5TU0NHk/nL77AuQGorq6mra1zq2xiYiL5+U4T\nTFVVVbcZWZOSksjLc0Z3VVZW4vV6O+IGSE5OJjfXaeKsqKjA5+vcopqSktLxn/PgwYPdbtOcmppK\ndrZzXVPX2Wghsp+98vLyjrgDevrsqUKLJjAsJ52MtJ4/ezk5OaSkpET1s9fY2EhiYmKvn72q+iY8\nTQ10bbHt6bMXEM3Pnt/vZ+RIp1Ycqc9esGh99gKf7/5+9u68887IDBsWkRk4zU557nIlcF1wX8fR\nIi4uruNDFhDJKcT/8pe/dNt+pFOI5+bmsmDBgqhOIZ6dnR3xKcQDv4SiOYV4tKavD/xHPZqmr3/y\nySe7/fI8GqavX79+PQUFBUfl9PWB1z/apq/PycmJ2vT14czltRKYF7Q8F1gZzrwug+0xefJkPdoM\ntTmDYs3iHlgW98CK+VxeQLqqLgtKQMuBo3rGYWOMMZEXziWWO0Tkv3CavQC+hDPzsDHGGNMhnBrK\nTTjzZ72CM+NwgbvOGGOM6dBnDUVVa4AjnbfLGGPMv7hw7in/hojkBC3nurP7GmOMMR3CafIqUNWO\nQehujSX0fVKNMcYMWeEkFL+IdMw+JyJjgfCuhjTGGDNkhDPK6y7gHRFZAQhwJu79RYwxxpiAcDrl\nF4vIbOBUd9V3VLX7HCPGGGOGtHBv9XU6cFbQcvd5HIwxxgxp4Yzyuhf4NvCR+/i2iPxPtAMzxhhz\ndAmnhnIxMEtV/QAi8jSwHvjPaAZmjDHm6BLOKC+A4GlMs6MRiDHGmKNbODWU/wXWi8gynFFeZwF3\nRjUqY4wxR51wRnk9LyLLgZPcVberave7BRljjBnSwumUX6qqB1R1ofsoF5Hud9vpBxHJc6d02eb+\nzQ1RZpaIrBKRLSLyoYh8IWjbUyKyU0Q2uI9ZRxKPMcaYI9djQhGRFBHJAwrc+bvy3Mc4oPgIj3sH\nsFRVJwFL3eWumnHuDDkdmA88FDynGHCbqs5yH91v52aMMWZA9dbk9VXgO8BIYF3Q+nrgV0d43AU4\nd34EeBpYDtweXEBVtwY93y8ih3Cm0e9+c2tjjDExJ6q9T8slIreq6i8jelCRWlXNcZ8LUBNY7qH8\nyTiJZ7qq+kXkKeA0wINbw1FVTw/73ow7VUxhYeGJ/bo/8iDQ2NhIRkZGrMPoN4t7YFncA2uoxT1v\n3ry1qjqnr3LhJJTrQq1X1Wf62G8JMCLEpruAp4MTiIjUqGq3fhR3WxFODeZ6VX0vaF05kAQ8CmxX\n1bt7fSPAlClTtKSkpK9ig8ry5cuZO3durMPoN4t7YFncA2uoxS0iYSWUcIYNnxT0PAU4F6cJrNeE\noqrn9RLcQREpUtUDbnI41EO5LODvwF2BZOK+9gH3qUdEngS+H8b7MMYYE0XhDBu+NXjZ7Rh/4QiP\nuxC4HrjX/fvXrgVEJAn4C/CMqr7cZVsgGQlwGbD5COMxxhhzhMK9Uj5YEzDhCI97L3C+iGwDznOX\nEZE5IvKYW+ZKnIsobwgxPPg5EdkEbMK5x/1PjzAeY4wxR6jPGoqI/I3DN9SKB44FjqhnW1WrcJrO\nuq5fA3zFff4s8GwP+59zJMc3xhgTeeH0oTwQ9NyLk1S+0ENZY4wxQ1Q4fSgrROQE4IvA54GdwJ+j\nHZgxxpijS48JRUQmA1e7j0rgRZxhxvMGKDZjjDFHkd5qKJ8AbwOfVdVSABH57oBEZYwx5qjT2yiv\ny4EDwDIR+b2InIszfb0xxhjTTY8JRVVfVdWrgKnAMpx5vYaJyG9E5IKBCtAYY8zRoc/rUFS1SVX/\nqKqXAKNwbv97ex+7GWOMGWL6dWGjqtao6qOq2u0aEmOMMUPbp7lS3hhjjOnGEooxxpiIsIRijDEm\nIiyhGGOMiQhLKMYYYyLCEooxxpiIsIRijDEmIiyhGGOMiQhLKMYYYyLCEooxxpiIiElCEZE8EXlD\nRLa5f3N7KOcLup/8wqD140XkfREpFZEXRSRp4KI3xhgTSqxqKHcAS1V1ErDUXQ6lRVVnuY9Lg9bf\nBzyoqhOBGuDL0Q3XGGNMX2KVUBYAT7vPnwYuC3dHERHgHODlT7O/McaY6BBVHfiDitSqao77XICa\nwHKXcl5gA+AF7lXVV0WkAHjPrZ0gIqOBf6jqjB6OdTNwM0BhYeGJL730UlTeU7Q0NjaSkZER6zD6\nzeIeWBb3wBpqcc+bN2+tqs7ps6CqRuUBLAE2h3gsAGq7lK3p4TWK3b8TgF3AMUABUBpUZjSwOZyY\nJk+erEebZcuWxTqET8XiHlgW98AaanEDazSM79je7il/RFT1vJ62ichBESlS1QMiUgQc6uE19rl/\nd4jIcuAE4M9AjogkqKoX56Zf+yL+BowxxvRLrPpQFgLXu8+vB/7atYCI5IpIsvu8ADgD+MjNlsuA\nK3rb3xhjzMCKVUK5FzhfRLYB57nLiMgcEXnMLXMssEZENuIkkHtV9SN32+3A90SkFMgHHh/Q6I0x\nxnQTtSav3qhqFdDtNsKqugb4ivt8JTCzh/13ACdHM0ZjjDH9Y1fKG2OMiQhLKMYYYyLCEooxxpiI\nsIRijDEmIiyhGGOMiQhLKMYYYyLCEooxxpiIsIRijDEmIiyhGGOMiQhLKMYYYyLCEooxxpiIsIRi\njDEmIiyhGGOMiQhLKMYYYyLCEooxxpiIsIRijDEmIiyhGGOMiQhLKMYYYyIiJglFRPJE5A0R2eb+\nzQ1RZp6IbAh6tIrIZe62p0RkZ9C2WQP/LowxxgSLVQ3lDmCpqk4ClrrLnajqMlWdpaqzgHOAZuCf\nQUVuC2xX1Q0DErUxxpgexSqhLACedp8/DVzWR/krgH+oanNUozLGGPOpxSqhDFfVA+7zcmB4H+Wv\nAp7vsu6/ReRDEXlQRJIjHqExxph+EVWNzguLLAFGhNh0F/C0quYEla1R1W79KO62IuBDYKSqtget\nKweSgEeB7ap6dw/73wzcDFBYWHjiSy+99OnfVAw0NjaSkZER6zD6zeIeWBb3wBpqcc+bN2+tqs7p\ns6CqDvgDKAGK3OdFQEkvZb8NPNrL9rnAonCOO3nyZD3aLFu2LNYhfCoW98CyuAfWUIsbWKNhfMfG\nqslrIXC9+/x64K+9lL2aLs1dbg0FERGc/pfNUYjRGGNMP8QqodwLnC8i24Dz3GVEZI6IPBYoJCLj\ngNHAii77Pycim4BNQAHw0wGI2RhjTC8SYnFQVa0Czg2xfg3wlaDlXUBxiHLnRDM+Y4wx/WdXyhtj\njIkISyjGGGMiwhKKMcaYiLCEYowxJiIsoRhjjIkISyjGGGMiwhKKMcaYiLCEYowxJiIsoRhjjIkI\nSyjGGGMiwhKKMcaYiLCEYowxJiIsoRhjjIkISyjGGGMiwhKKMcaYiLCEYowxJiIsoRhjjIkISyjG\nGGMiwhKKMcaYiIhJQhGRz4vIFhHxi8icXsrNF5ESESkVkTuC1o8Xkffd9S+KSNLARG6MMaYnsaqh\nbAYuB97qqYCIxAOPABcB04CrRWSau/k+4EFVnQjUAF+ObrjGGGP6EpOEoqofq2pJH8VOBkpVdYeq\ntgEvAAtERIBzgJfdck8Dl0UvWmOMMeFIiHUAvSgG9gYtlwGnAPlArap6g9YX9/QiInIzcLO76BGR\nzVGINZoKgMpYB/EpWNwDy+IeWEMt7rHhFIpaQhGRJcCIEJvuUtW/Ruu4Xanqo8CjbkxrVLXHPpvB\n6GiMGSzugWZxDyyLO7SoJRRVPe8IX2IfMDpoeZS7rgrIEZEEt5YSWG+MMSaGBvOw4Q+ASe6IriTg\nKmChqiqwDLjCLXc9MGA1HmOMMaHFatjw50SkDDgN+LuIvO6uHykirwG4tY9bgNeBj4GXVHWL+xK3\nA98TkVKcPpXHwzz0oxF8GwPlaIwZLO6BZnEPLIs7BHF+8BtjjDFHZjA3eRljjDmKWEIxxhgTEUMi\nofQ0hctgICKjRWSZiHzkTkfzbXd9noi8ISLb3L+57noRkV+47+VDEZkdw9jjRWS9iCxyl0NOiSMi\nye5yqbt9XAxjzhGRl0XkExH5WEROO0rO9Xfdz8dmEXleRFIG4/kWkSdE5FDw9V6f5vyKyPVu+W0i\ncn2M4v6Z+zn5UET+IiI5QdvudOMuEZELg9YP6HdNqLiDtv0/EVERKXCXo3++VfVf+gHEA9uBCUAS\nsBGYFuu4guIrAma7zzOBrThTzdwP3OGuvwO4z31+MfAPQIBTgfdjGPv3gD8Ci9zll4Cr3Oe/Bb7u\nPv8G8Fv3+VXAizGM+WngK+7zJCBnsJ9rnAt3dwKpQef5hsF4voGzgNnA5qB1/Tq/QB6ww/2b6z7P\njUHcFwAJ7vP7guKe5n6PJAPj3e+X+Fh814SK210/GmdA026gYKDO94D/5xjoB85IsteDlu8E7ox1\nXL3E+1fgfKAEKHLXFQEl7vPfAVcHle8oN8BxjgKW4kyDs8j9kFYG/QfsOO/uB/s093mCW05iEHO2\n+8UsXdYP9nMdmDUizz1/i4ALB+v5BsZ1+WLu1/kFrgZ+F7S+U7mBirvLts8Bz7nPO32HBM53rL5r\nQsWNMzXV8cAuDieUqJ/vodDkFWoKlx6naoklt2niBOB9YLiqHnA3lQPD3eeD5f08BPwA8LvLvU2J\n0xGzu73OLT/QxgMVwJNuU91jIpLOID/XqroPeADYAxzAOX9rGfznO6C/53dQnPcubsL5dQ+DPG4R\nWQDsU9WNXTZFPe6hkFCOCiKSAfwZ+I6q1gdvU+dnw6AZ3y0inwUOqeraWMfSTwk4zQO/UdUTgCac\nJpgOg+1cA7h9DgtwEuJIIB2YH9OgPqXBeH77IiJ3AV7guVjH0hcRSQP+E/hhLI4/FBJKT1O4DBoi\nkoiTTJ5T1Vfc1QdFpMjdXgQcctcPhvdzBnCpiOzCmQX6HOBh3ClxQsTVEbO7PRtnCp2BVgaUqer7\n7vLLOAlmMJ9rgPOAnapaoartwCs4/waD/XwH9Pf8DpbzjojcAHwWuMZNhjC44z4G54fHRvf/5yhg\nnYiM6CW+iMU9FBJKyClcYhxTBxERnCv9P1bVnwdtWogzrQx0nl5mIXCdO2LjVKAuqDlhQKjqnao6\nSlXH4ZzPN1X1GnqeEif4vVzhlh/wX6mqWg7sFZEp7qpzgY8YxOfatQc4VUTS3M9LIO5Bfb6D9Pf8\nvg5cICK5bu3sAnfdgBKR+TjNupeqanPQpoXAVe5ouvHAJGA1g+C7RlU3qeowVR3n/v8swxn0U85A\nnO9odxgNhgfO6IatOCMw7op1PF1i+wxOE8CHwAb3cTFOm/dSYBuwBMhzywvOjce2A5uAOTGOfy6H\nR3lNwPmPVQr8CUh216e4y6Xu9gkxjHcWsMY936/ijGoZ9Oca+AnwCc7N6f6AM8Jo0J1v4Hmcfp52\nnC+zL3+a84vTZ1HqPm6MUdylOH0Lgf+Xvw0qf5cbdwlwUdD6Af2uCRV3l+27ONwpH/XzbVOvGGOM\niYih0ORljDFmAFhCMcYYExGWUIwxxkSEJRRjjDERYQnFGGNMRFhCMWYAiEhjrGMwJtosoRhjjIkI\nSyjGxIiIXOLer2S9iCwRkeHu+kL3viFb3AksdwfuaWHMYGYJxZjYeQc4VZ2JKl/AmeYD4Ec406VM\nx5lvbEyM4jOmXxL6LmKMiZJRwIvuhIlJOPdqAWc6ns8BqOpiEamJUXzG9IvVUIyJnV8Cv1LVmcBX\ncebgMuaoZQnFmNjJ5vA04cH38X4XuBJARC7AmcDSmEHPJoc0ZgCIiB/YH7Tq5zizvj4I1ABvAiep\n6lwRGYYzi+xwYBXO/TjGqapnYKM2pn8soRgzyIhIMuBTVa+InIZzh8lZsY7LmL5Yp7wxg88Y4CUR\niQPagP+IcTzGhMVqKMYYYyLCOuWNMcZEhCUUY4wxEWEJxRhjTERYQjHGGBMRllCMMcZExP8Hb/2t\neVCOXRcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "ddRJGI1pic78",
        "outputId": "43ce8d06-1bc8-414c-b264-b0b3dd6ca260",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        }
      },
      "source": [
        "from statsmodels.tsa.arima_model import ARIMA\n",
        "\n",
        "model = ARIMA(series, order=(5, 1, 0))\n",
        "model_fit = model.fit(disp=0)\n",
        "print(model_fit.summary())\n"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                             ARIMA Model Results                              \n",
            "==============================================================================\n",
            "Dep. Variable:                    D.y   No. Observations:                 1460\n",
            "Model:                 ARIMA(5, 1, 0)   Log Likelihood                2223.428\n",
            "Method:                       css-mle   S.D. of innovations              0.053\n",
            "Date:                Sat, 24 Aug 2019   AIC                          -4432.855\n",
            "Time:                        15:43:17   BIC                          -4395.852\n",
            "Sample:                             1   HQIC                         -4419.052\n",
            "                                                                              \n",
            "==============================================================================\n",
            "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          0.0003      0.001      0.384      0.701      -0.001       0.002\n",
            "ar.L1.D.y     -0.1235      0.026     -4.714      0.000      -0.175      -0.072\n",
            "ar.L2.D.y     -0.1254      0.029     -4.333      0.000      -0.182      -0.069\n",
            "ar.L3.D.y     -0.1089      0.029     -3.759      0.000      -0.166      -0.052\n",
            "ar.L4.D.y     -0.0914      0.029     -3.162      0.002      -0.148      -0.035\n",
            "ar.L5.D.y     -0.0774      0.029     -2.675      0.008      -0.134      -0.021\n",
            "                                    Roots                                    \n",
            "=============================================================================\n",
            "                  Real          Imaginary           Modulus         Frequency\n",
            "-----------------------------------------------------------------------------\n",
            "AR.1            1.0145           -1.1311j            1.5194           -0.1336\n",
            "AR.2            1.0145           +1.1311j            1.5194            0.1336\n",
            "AR.3           -1.8173           -0.0000j            1.8173           -0.5000\n",
            "AR.4           -0.6967           -1.6113j            1.7554           -0.3150\n",
            "AR.5           -0.6967           +1.6113j            1.7554            0.3150\n",
            "-----------------------------------------------------------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "A0l79ROF1xu1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 409
        },
        "outputId": "03c287fc-61c6-4693-b006-af396fd6d82d"
      },
      "source": [
        "df = pd.read_csv(\"sunspots.csv\", parse_dates=[\"Date\"], index_col=\"Date\")\n",
        "series = df[\"Monthly Mean Total Sunspot Number\"].asfreq(\"1M\")\n",
        "series.head()"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "error",
          "ename": "FileNotFoundError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-29-3ef4403be25e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"sunspots.csv\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparse_dates\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"Date\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex_col\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"Date\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mseries\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"Monthly Mean Total Sunspot Number\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masfreq\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"1M\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mseries\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhead\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36mparser_f\u001b[0;34m(filepath_or_buffer, sep, delimiter, header, names, index_col, usecols, squeeze, prefix, mangle_dupe_cols, dtype, engine, converters, true_values, false_values, skipinitialspace, skiprows, skipfooter, nrows, na_values, keep_default_na, na_filter, verbose, skip_blank_lines, parse_dates, infer_datetime_format, keep_date_col, date_parser, dayfirst, iterator, chunksize, compression, thousands, decimal, lineterminator, quotechar, quoting, doublequote, escapechar, comment, encoding, dialect, tupleize_cols, error_bad_lines, warn_bad_lines, delim_whitespace, low_memory, memory_map, float_precision)\u001b[0m\n\u001b[1;32m    700\u001b[0m                     skip_blank_lines=skip_blank_lines)\n\u001b[1;32m    701\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 702\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_read\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    703\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    704\u001b[0m     \u001b[0mparser_f\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m_read\u001b[0;34m(filepath_or_buffer, kwds)\u001b[0m\n\u001b[1;32m    427\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    428\u001b[0m     \u001b[0;31m# Create the parser.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 429\u001b[0;31m     \u001b[0mparser\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTextFileReader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    430\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    431\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mchunksize\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0miterator\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, f, engine, **kwds)\u001b[0m\n\u001b[1;32m    893\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'has_index_names'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'has_index_names'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    894\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 895\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_make_engine\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mengine\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    896\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    897\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m_make_engine\u001b[0;34m(self, engine)\u001b[0m\n\u001b[1;32m   1120\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_make_engine\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mengine\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'c'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1121\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'c'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1122\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mCParserWrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1123\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1124\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'python'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, src, **kwds)\u001b[0m\n\u001b[1;32m   1851\u001b[0m         \u001b[0mkwds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'usecols'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0musecols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1852\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1853\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reader\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mparsers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTextReader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1854\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munnamed_cols\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reader\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munnamed_cols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1855\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32mpandas/_libs/parsers.pyx\u001b[0m in \u001b[0;36mpandas._libs.parsers.TextReader.__cinit__\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;32mpandas/_libs/parsers.pyx\u001b[0m in \u001b[0;36mpandas._libs.parsers.TextReader._setup_parser_source\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] File b'sunspots.csv' does not exist: b'sunspots.csv'"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "wVoq4cmx3-vk",
        "colab": {}
      },
      "source": [
        "series.plot(figsize=(12, 5))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "stmDLe8jEDQL",
        "colab": {}
      },
      "source": [
        "series[\"1995-01-01\":].plot()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "SXc9PkCXJd_a",
        "colab": {}
      },
      "source": [
        "series.diff(1).plot()\n",
        "plt.axis([0, 100, -50, 50])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "G1T-V7B8180O",
        "colab": {}
      },
      "source": [
        "from pandas.plotting import autocorrelation_plot\n",
        "\n",
        "autocorrelation_plot(series)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "8jdIxEASH_1z",
        "colab": {}
      },
      "source": [
        "autocorrelation_plot(series.diff(1)[1:])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "6eIY8wloG3Go",
        "colab": {}
      },
      "source": [
        "autocorrelation_plot(series.diff(1)[1:].diff(11 * 12)[11*12+1:])\n",
        "plt.axis([0, 500, -0.1, 0.1])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "El2JSNZwG7UP",
        "colab": {}
      },
      "source": [
        "autocorrelation_plot(series.diff(1)[1:])\n",
        "plt.axis([0, 50, -0.1, 0.1])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "gvmZAKeAHACf",
        "colab": {}
      },
      "source": [
        "116.7 - 104.3"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "ReEbS1MpC50n",
        "colab": {}
      },
      "source": [
        "[series.autocorr(lag) for lag in range(1, 50)]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "7rdXm2UX3WsH",
        "colab": {}
      },
      "source": [
        "pd.read_csv(filepath_or_buffer, sep=',', delimiter=None, header='infer', names=None, index_col=None, usecols=None, squeeze=False, prefix=None, mangle_dupe_cols=True, dtype=None, engine=None, converters=None, true_values=None, false_values=None, skipinitialspace=False, skiprows=None, skipfooter=0, nrows=None, na_values=None, keep_default_na=True, na_filter=True, verbose=False, skip_blank_lines=True, parse_dates=False, infer_datetime_format=False, keep_date_col=False, date_parser=None, dayfirst=False, iterator=False, chunksize=None, compression='infer', thousands=None, decimal=b'.', lineterminator=None, quotechar='\"', quoting=0, doublequote=True, escapechar=None, comment=None, encoding=None, dialect=None, tupleize_cols=None, error_bad_lines=True, warn_bad_lines=True, delim_whitespace=False, low_memory=True, memory_map=False, float_precision=None)\n",
        "Read a comma-separated values (csv) file into DataFrame.\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "sYXNHu_trIH2",
        "colab": {}
      },
      "source": [
        "from pandas.plotting import autocorrelation_plot\n",
        "\n",
        "series_diff = series\n",
        "for lag in range(50):\n",
        "  series_diff = series_diff[1:] - series_diff[:-1]\n",
        "\n",
        "autocorrelation_plot(series_diff)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "s6SVHBpqrO1X",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "\n",
        "series_diff1 = pd.Series(series[1:] - series[:-1])\n",
        "autocorrs = [series_diff1.autocorr(lag) for lag in range(1, 60)]\n",
        "plt.plot(autocorrs)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}